Question

Use the long division method to find the result when 3x^(3)+10x^(2)-5x-23 is divided by 3x+7. If there is a remainder, express the result in the form q(x)+(r(x))/(b(x))

Answer 1

Using long division, the polynomial 3x^3 + 10x^2 - 5x - 23 is divided by 3x + 7 step by step, which involves dividing terms, multiplying, and subtracting to find the quotient and possibly a remainder in the form q(x) + r(x)/b(x).

Step-by-step explanation:

To divide 3x^3 + 10x^2 - 5x - 23 by 3x + 7 using the long division method, you perform the following steps:

1. Divide the first term of the dividend (3x^3) by the first term of the divisor (3x) to get the first term of the quotient, which is x^2.
2. Multiply the entire divisor by x^2 and subtract this from the dividend.
3. Bearing in mind division of exponentials, bring down the next term from the original dividend and repeat the process until all terms have been accounted for.
4. If there is a remainder after the last subtraction, express the result in the form of the quotient plus the remainder over the divisor.

Through this process, you would find the quotient and the remainder, and the final answer would be expressed as q(x) + r(x)/b(x).